Scheme for Teleportation of Quantum States onto a Mechanical Resonator

We propose an experimentally feasible scheme to teleport an unkown quantum state onto the vibrational degree of freedom of a macroscopic mirror. The quantum channel between the two parties is established by exploiting radiation pressure effects.

Figure 1

Schematic description of the system. A laser field at frequency ${\omega }_0$ impinges on the mirror oscillating at frequency $\Omega$. In the reflected field two sideband modes are excited at frequencies ${\omega }_1={\omega }_0-\Omega$ and ${\omega }_2={\omega }_0+\Omega$. These two modes then reach Alice’s station. The mode at frequency ${\omega }_2$ is subjected to a heterodyne measurement $D2$, while the mode at frequency ${\omega }_1$ is mixed in the 50-50 beam splitter BS with the unknown input given by Victor. A Bell-like measurement $D1$ is then performed on this combination and the result, combined with the heterodyne one, is fed-forward to Bob. Finally, he actuates the displacement in the phase space of the moving mirror.

Figure 2

Fidelity $F$ vs the scaled time $\Theta t$, being $\Theta =\sqrt{{\theta }^2-{\chi }^2}$. Curves $a$, $b$, $c$, $d$ are for $\overline{n}=0$, 1, 10, ${10}^3$, respectively. The values of parameters are $\wp =10\mathrm{W}$; $\Omega =5\times {10}^8\mathrm{H}\mathrm{z}$; $\Delta {\nu }_{\det }={10}^7\mathrm{H}\mathrm{z}$; $M={10}^{-10}\mathrm{K}\mathrm{g}$; ${\omega }_0=2\times {10}^{15}\mathrm{H}\mathrm{z}$, $\Delta {\nu }_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}}={10}^3\mathrm{H}\mathrm{z}$.